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User blog:Primussupremus/A brief introduction to the philosophy of numbers.
This article may be unusual too many people as it will go against many of their views of what a number is but it will not go against many of their other beliefs , I hope that people will learn something of value from this if not then at least it will let you look at the world in a different light. If this statement sounded really trippy well it wasn't intended to be. Well lets begin: Suppose that you are walking along the street and suddenly a man comes up to you and says , "what is a number?" Your first response might be to give an example like this "their are 5 apples so this has the quality of 5". Now this person being a philosophical creature thinks "well that can't be right how do 5 objects represent the number 5 in its purity". This person was correct to say that representing a number using objects is an ill description of what it means to be a number. After speaking to this person for a bit longer you decide to return home to think about the nature of numbers for a bit longer. You eventually come to the conclusion that numbers don't exist in the sense that we can't directly perceive them , but they do exist in the sense that we require them to live our daily lives. If that was confusing I will explain, a number is a symbol that is used to represent a quantity in some type of calculation. You then ask yourself what is the smallest meaning quantity that will still provide some type of meaningful result? Is is it 1? or is it 1/2? or is it 1/256? after going through a gigantic list of fractions you decide to give up. Suddenly a thought hits your head maybe the smallest positive value is 0? You then decide to perform a series of division sums to reach your desired answer of 0 , you start off with 1/2/3/4/5/6/7/8/9/10... until you have got up to the 10^5000th term but still you don't get the answer you desire. Even if you did this for a countably infinite number of years you still wouldn't reach the exact answer of 0 always be close but yet to far. You then conclude that their is no smallest positive number that can be constructed purely from division , your next thought is to use the negative integers to see what they can produce. After continuing down through the negatives you come to realize that even they have no limit. You already know that the positive integers must tend towards infinity as you can always input a number k into the successor function and produce out k+1. After concluding that the natural numbers and integers are both infinite in size you decide to see whether or not the rational numbers are infinite as well. Yet again you come to to conclusion that the rational numbers are in fact still infinite in magnitude. You even conclude that the irrational numbers like pi and e are again still in infinite in magnitude. You then conclude that even the transcendental numbers like pi are again infinite in size. After spending a few days pondering on the infinite size of the numbers you conclude that all the different types of numbers from natural numbers to surreal numbers are indeed infinite. You then ask yourself if some infinities are bigger than others then what is limit to these infinities? Eventually you conclude this limit must be true infinity or absolute infinity. This absolute infinity is completely inaccessible as it is impossible to define true infinity using the standard axioms of mathematics. Category:Blog posts